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Common aspects of q-deformed Lie algebras and fractional calculus

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  • Herrmann, Richard

Abstract

Fractional calculus and q-deformed Lie algebras are closely related. Both concepts expand the scope of standard Lie algebras to describe generalized symmetries. A new class of fractional q-deformed Lie algebras is proposed, which for the first time allows a smooth transition between different Lie algebras.

Suggested Citation

  • Herrmann, Richard, 2010. "Common aspects of q-deformed Lie algebras and fractional calculus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4613-4622.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:21:p:4613-4622
    DOI: 10.1016/j.physa.2010.07.004
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    References listed on IDEAS

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    1. Herrmann, Richard, 2010. "Higher-dimensional mixed fractional rotation groups as a basis for dynamic symmetries generating the spectrum of the deformed Nilsson oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(4), pages 693-704.
    2. Goldfain, Ervin, 2006. "Complexity in quantum field theory and physics beyond the standard model," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 913-922.
    3. Herrmann, Richard, 2010. "Fractional phase transition in medium size metal clusters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3307-3315.
    4. Tarasov, Vasily E. & Zaslavsky, George M., 2006. "Dynamics with low-level fractionality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(2), pages 399-415.
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